Greens housing spokesman Max Chandler-Mather has accused Anthony Albanese of spreading lies about him as the debate over the government’s centrepiece housing policy takes another acrimonious turn.

Behind closed doors, the minor party and Labor have returned to the negotiating table to try to thrash out a compromise on the Housing Australia Future Fund before parliament returns in June.

Labor last week failed in its effort to wedge the Greens, who hold the balance of power in the Senate, trying unsuccessfully to bring on a vote on the legislation to set up the $10bn investment vehicle without having struck a deal with the minor party.

MPs from both parties have engaged in a public war of words as they accuse each other of “playing politics” over the stalemate, with the Prime Minister repeatedly taking aim at the Greens at recent press conferences.

Mr Albanese on Tuesday said Mr Chandler-Mather was petitioning against medium-density housing being built in his Griffith electorate in Brisbane at the same time as he was blocking the HAFF in parliament.

“You can’t have it both ways,” he told reporters.

Mr Chandler-Mather disputed Mr Albanese’s claim later on Tuesday, saying it was “dismaying” to see the Prime Minister “shift towards personal attacks and lies about me”.

Speaking to reporters in Brisbane, Mr Chandler-Mather said the fresh round of negotiations with the government on the HAFF legislation was yet to bear fruit and the Greens were still willing to vote the Bill down.

But he signalled the minor party was willing to bend on its two key demands.

The Greens want the government to guarantee $5bn in investment every year, indexed to inflation, for social and affordable housing, as well as commonwealth incentives for the states and territories to freeze rent increases under their respective legislation.

“I would still say that we’re willing to go below both of those demands and negotiate in good faith,” he said.

Asked what amendments the Greens would accept as a minimum, Mr Chandler-Mather said he wouldn’t put a “red line” under what they want in return for their crucial Senate votes.

“But it takes two to tango. And we really desperately need now the government to come to the table and try to work out how we can meet halfway.”

Labor says up to $500m a year worth of returns from the $10bn investment vehicle will be spent on building social and affordable housing, with a promise of 30,000 homes in its first five years and at least 1200 homes a year for each state and territory.